Name:______________________________________________________________
Math 3311
Assignment: Linear relationships
1. Calculate the first difference in x and y, then write the linear equation:
Change in x
x
f(x)
-6
--3
-3
2
0
7
3
12
6
17
9
22
12
27
Change in y
Your slope:
Your equation:
2. Calculate the first difference in x and y, then write the linear equation:
Change in x
Your slope:
Your equation:
x
f(x)
-4
-45/7
-2
-33/7
0
-3
2
-9/7
4
3/7
6
15/7
8
27/7
Change in y
3. Is the relation of this data linear? If so, write an equation modeling the relationship.
Change in x
x
f(x)
0
1.44
2
3.34
7
8.09
10
10.94
Change in f(x)
***Since the change in x is not uniform, do you think you need to compute the slope on each interval?
4. Is the relation of this data linear? If so, write an equation modeling the relationship.
Change in x
Altitude
x, thousands of feet
8
Temperature, o F
f(x)
197.6
4.5
203.9
3
206.6
2.5
207.5
Change in f(x)
5. A recursive function defines a function by referring to the value of the function at previous whole numbers (the
domain is always whole numbers). Consider the recursive function f (n)  f (n  1)  5 with f (0)  1 .
Determine whether the function is linear on its domain. If so, write an algebraic expression for f(n) as a function of n.
Name:______________________________________________________________
Math 3311
Assignment: Quadratic and cubic relationships
Use first, second, and third differences to determine whether the function is linear, quadratic, or cubic.
Write the equation describing the function.
1.
 3, 7 ,  0, 2 , 3, 7 , 6, 34 , 9, 79
2.
3,1 , 5, 3 , 7, 7  , 9, 11 , 11, 15
3.
 8, 2 ,  5,7 ,  2,12 , 1,17  ,  4, 22
4.
 6,146 ,  3,17 , 0, 4 , 3, 25 , 6,154 , 9, 499 , 12,1168
5. Calculate the first and second differences.
Is the relation quadratic? Explain your answer.
x
f(x)
3
2
7
6
10
12
14
20
17
30
First Difference
Second Difference
7. Write an equation for a quadratic function having uniform second differences of 6 and passing through the point
(1,5).


1
3
8. Write an equation for a cubic function having uniform third differences of 1 and passing through the point  2, 
9. The table below shows the annual sales of a small corporation over a period of years:
Year
Sales
2006
$513,000
2007
$516,000
2008
$521,000
2009
$528,000
2010
$537,000
A. Write a function to model the data.
B. In what year will sales increase $17,000 from the previous year?
Name:______________________________________________________________
Math 3311
Assignment: Exponential and logarithmic relationships
Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
 1   1   1   1   1  
 ,  7,  ,  9,

 2   6   18   54   162  
1. 1,  ,  3,  ,  5,
2.
 0,1 , 1,3 ,  2,9 , 3,19 ,  4,33
3.
x
f(x)
0
600
10
480
20
384
30
307.2
40
245.76
Your function:
First Difference
Second Difference
Third Difference
4. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
x
f(x)
-2
.75
0
3
2
12
4
48
6
192
First Difference
Second Difference
Third Difference
Your equation:
5. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
x
f(x)
1
1
3
3
9
5
27
7
81
9
Your equation:
First Difference
Second Difference
Third Difference
6. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
x
f(x)
1
5
4
6
16
7
32
7.5
64
8
First Difference
Second Difference
Third Difference
Your equation:
7. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
x
f(x)
0
5
1
10
2
20
3
40
4
80
Your equation:
First Difference
Second Difference
Third Difference
8 .Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.
x
f(x)
-1
.04
1
1
3
25
5
625
7
15625
First Difference
Second Difference
Third Difference
Your equation:
9.
A) Complete the table so the relation is a linear function:
0
1
x
f(x)
3
3
3
4
2
3
4
2
3
4
6
C) Complete the table so the relation is an exponential function:
0
1
x
f(x)
3
6
B) Complete the table so the relation is a quadratic function:
0
1
x
f(x)
2
6
For which of the above types of functions (linear, quadratic, exponential) is there more than one correct way to
complete the table??? Explain.